a.  Explain how to determine whether you should shade above or below a boundary line on the graph of an inequality. [1 mark]

 

b. John is working to earn money to go on a ski trip. He wants to save at least $480. John works at the local swimming pool and makes $40 per hour lifeguarding and $20 per hour teaching swimming lessons.

i. Determine an inequality that would represent this situation. [1 mark]

 

ii. Draw a graph of the inequality to show the number of hours spent working at each task so that John can earn at least $480 for his ski trip.[2 marks]Click here for a pdf of a blank grid to print off.

iii. Select a test point above the boundary, explain using the graph whether the test point is part of the solution. [1 mark]

 

 

iv.  Select a test point below the boundary, verify algebraically whether the test point is part of the solution. [1 mark]

4 years ago

Answered By Swapan S

Let x = number of hours for lifeguarding 

Let y = number of hours for swimming lessons 

Assumption: Both can not be done together 

i.    $40x+20y\ge\text{480}$40x+20y≥480   

ii. refer graph

iii. Lets Select a test point at x=4, If x=4, substituting the value in  $2x+y\ge12$2x+y≥12 

 $y\ge4$y≥4 

at x=4 and  $y\ge4$y≥4 

$>= 480$

 

Attached Graph:

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4 years ago

Answered By Manasa R

To figure out whether you should shade above or below, you cant test point values into the inequality and see where they land (based on the question), and if its above, you shade above, if its below, you shade below.

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